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Strong Implication-Form ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems

Abstract : Input-to-State Stability (ISS) and the ISS-Lyapunov function have proved to be useful tools for the analysis and design of nonlinear systems in a variety of contexts. Motivated by the fact that many feedback control laws, such as model predictive control or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov func-tions were originally introduced in a so-called implication-form and, in many cases, this has been shown to be equivalent to an ISS-Lyapunov function of dissipation-form. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implication-form ISS-Lyapunov which re-establishes the equivalence to dissipation-form ISS-Lyapunov functions and to the ISS property for discontinuous systems.
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https://hal.inria.fr/hal-01098331
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Submitted on : Tuesday, December 23, 2014 - 5:42:06 PM
Last modification on : Friday, October 13, 2017 - 5:08:16 PM
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  • HAL Id : hal-01098331, version 1

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Lars Grüne, Christopher M. Kellett. Strong Implication-Form ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems. MTNS 2014, 2014, Groningen, Netherlands. pp.1023-1030. ⟨hal-01098331⟩

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